Table Of ContentInsurance and Risk Theory
NATO ASI Series
Advanced Science Institutes Series
A series presenting the results of activities sponsored by the NA TO Science Committee,
which aims at the dissemination of advanced scientific and technological knowledge,
with a view to strengthening links between scientific communities.
The series is published by an international board of publishers in conjunction with the
NATO Scientific Affairs Division
A Life Sciences Plenum Publishing Corporation
B Physics London and New York
C Mathematical D. Reidel Publishing Company
and PhYSical Sciences Dordrecht, Boston, Lancaster and Tokyo
D Behavioural and Social Sciences Martinus Nijhoff Publishers
E Engineering and The Hague, Boston and Lancaster
Materials Sciences
F Computer and Systems Sciences Springer-Verlag
G Ecological Sciences Berlin, Heidelberg, New York and Tokyo
Series C: Mathematical and Physical Sciences Vol. 171
Insurance and
Risk Theory
edited by
M. Goovaerts
Catholic University of Louvain, Belgium and
The University of Amsterdam, The Netherlands
F. de Vylder
Catholic University of Louvain, Belgium
and
J.Haezendonck
University of Antwerp, Belgium
D. Reidel Publishing Company
Dordrecht / Boston / Lancaster / Tokyo
Published in cooperation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Study Institute on
Insurance and Risk Theory
Maratea, Italy
15-25 July, 1985
Library of Congress Cataloging in Publication Data
NATO Advanced Study Institute on Insurance and Risk Theory (1985: Maratea, Italy)
Insurance and risk theory.
(NATO ASI series. Series C, Mathematical and physical sciences; vol. 171)
"Sponsored by the NATO Science Committee"
"Published in cooperation with NATO Scientific Affairs Division."
Includes index.
1. Risk (I nsurance)-Congresses. I. Goovaerts, M. J., 1946- II. Vylder,
Florent de. III. Haezendonck, J., 1940- . IV. NATO Science Committee. V.
Title. VI. Series: NATO ASI series. Series C, Mathematical and phYSical sciences; vol. 171.
HG8054.5.N38 1985 368 86-416
ISBN-13 :978-94-01 0-8553-3 e-ISBN-13: 978-94-009-4620-0
001: 10. 1007/978-94-009-4620-0
Published by D. Reidel Publishing Company
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In all other countries, sold and distributed
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D. Reidel Publishing Company is a member of the Kluwer Academic Publishers Group
All Rights Reserved
© 1986 by D. Reidel Publishing Company, Dordrecht, Holland.
Softcover reprint of the hardcover 1st edition 1986
No part of the material protected by this copyright notice may be reproduced or utilized
in any form or by any means, electronic or mechanical, including photocopying, recording
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copyright owner.
TABLE OF CONTENTS
Scientific committee and co-sponsors ix
Scientific contents of the course xi
Acknowledgement xii
Opening session
Invited lecture
Risk Theory, a Tool for Management?
G.W. de Wit 3
Main lectures
Economic Ideas in Risk Theory
H ,U. Gerber 25
Simulation in Insurance
E. Pitacco 37
Application of the Problem of Moments to Various
Insurance Problems in Non-life
R. Kaas and M.J. Goovaerts 79
Application of Martingales in Risk Theory
F. Delbaen and J. Haezendonck 119
Applications of Operations-Research Techniques in
Insurance
A.F. Shapiro 129
Recent Research on the Risk Return Relationship
in Financial Economics
P.P. Boyle 145
General Regression in Multidimensional Credibility Theory
F. De Vylder 165
Ruin Theory under the Submartingale Assumption
F. Moriconi 177
vi TABLE OF CONTENTS
A rigorous Proof of a Property of the Premium Principle
of Zero Utility in the Case of Additivity
V. Mammitzsch 189
Bayesian Credibility with a Noninformative Prior
S.A. Klugman 195
Short communications
Separation Theorems in Proportional Reinsurance
F. Pres sacco 209
A new Treatment of the En~ineering Aspects of the "Zero-Infinity
Dilemmas" of Industrial Risk Management
D.H. Critchley 217
On a Functional-Differential Equation connected with the
Premium Principle of Zero Utility
H. Si tter 235
Markov Processes between Moving Barriers - Mo~ents of the first
Hitting Time of fl~taining or Absorbing Barrier
W. Ettl 239
Some Mathematical Aspects of Combining Proportional and
Non-Proportional Reinsurance
L. Centeno 247
The Moments of Compound Interest Functions when Interest
fluctuates as a Compound Markov Chain
C.M. Ramsay 267
Pension Funding and random Rates of Return
D. Dufresne 277
Baye~ Criterion, the Minimax Principle and Statistical
Decision Theory
H.M. Fisuno!!lu 293
Large Claims -
M.I. Gomes and D.O. Pestana 301
Some Numerical Methods for Calculating Semi linear
Credibility Estimators
M. Van Wouwe, F. De Vylder and M. Goovaerts 325
Weak Convergence of Risk Processes
J. Garrido 34S
On the Exposed to Risk Theory
L. Siga lotti 361
TABLE OF CONTENTS vii
Probability Bounds on Compound Distributions with given
Moments on Claim Severities
M. Vandebroek, D. Gysels and M. Goovaerts 367
Additivity and Premium Calculation Principles
B. Heijnen and M.J. Goovaerts 373
Computing Moments of Compound Distributions
R. Kaas and M.J. Goovaerts 381
Portfolio Valuation in Life Insurance
A.R. Bacinello 385
Risk Assessment of Merger, Acquisition, and Consolidation
of Financial Services
B. Chan 401
Extending Arrow-Pratt Risk Premiums
H. Schlesinger 407
On Optimal Deductibles
W.-R. Heilmann 421
Solvency Margin and Profit in Life Insurance
E. Pitacco 435
Statistical Methods in General Insurance
P. Carroll 447
Modelling Motor Insurance Claim Frequencies
K. Stroinski 453
General Bounds on Ruin Probabilities
R. Kaas, M. Goovaerts and R. De Ridder 459
Strict Liability and Insurance under Loss Misestimation
R. Yaksick 465
Index 481
Scientific committee
C. Angela Mormino (Italy), P. Artzner (France), P. Boyle (Canada),
L. oaboni (Italy), J. De Broux (Belgium), F. oelbaen (Belgium),
G.W. de Wit (The Netherlands), H. Gerber (Switzerland), E. Helten
(F.R. Germany), W. Jewell (U.S.A.), S. Klugman (U.S.A.),
V. Mammitzsch (F.R. Germany), E. Pitacco (Italy), A. Shapiro (U.S.A.),
J. Teugels (Belgium), O. Wilkie (United Kingdom).
Co-sponsors
- B.V.V.O.
(Professional Association of Belgian Insurance Companies)
- LA.W.
(Institute of Actuarial Sciences of Leuven)
- Oepartement of Mathematics and Computer Science of the
University of Antwerp, UIA.
- Consiglio Nazionale delle Ricerche (Italy)
ix
SCIENTIFIC CONTENTS OF THE COURSE
The Nato Advanced Study Institute on Insurance and Risk Theory is a
continuation of the Nato Advanced Study Institute on Premium Calcula
tion in Insurance held in Leuven, Belgium (July 19S3). During the
previous NATO ASI most of the participants and especially the Amer~can
lecturers have expressed the wish of the organization of a ASI on
Insurance and Risk Theory.
The subject covers a field of considerable interest. The risk-theore
tical point of view in insurance is the main concern of the present
contribution to the actuarial literature. The subject is not treated
specifically actuarial, but rather embraces all aspects of the mathe
matics of risk situations.
Currently insurance research tends to be fragmented for two main
reasons. Firstly the heavy emphasis by English speaking actuaries
in life insurance and retirement funding is noticable in contrast
with the greater emphasis by continental actuaries on risk theory
and generally more mathematical endeavour. The NATO A.S.I. on In
surance and Risk Theory surmounts these national barriers. Secondly
the gap between theoreticians and practitioners is lessened. Apart
from topics such as credibility theory, loss reserves by way of so
called "run-off triangles", calculation of ruin probabilities, premium
principles, simUlation techniques, we are very happy with some in
teresting contributions, lectures as well as short communications, on
the attractive field of insurance economics which of course represents
an implicit suggestion for a future NATO Advanced Study Institute.
The Directors
M. Goovaerts
J. Haezendonck
F. De Vylder
xi
ACKNOWLEDGEMENT
We are grateful to the Scientific Affairs Division of NATO for the
financial assistance, and to Dr. C. Sinclair for his assistance and
support.
xii
